To prove that △DFE ~ △GFH by SAS similarity theorem, then option C. ∠DFE is congruent to ∠GFH is appropriate. So that: [tex]\dfrac{DF}{GF}[/tex] =[tex]\dfrac{EF}{HF}[/tex] and ∠DFE is congruent to ∠GFH.The correct answer is option C.
The image of the triangle is attached with the answer below:-
What is congruency?
The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
Given ΔDEF as shown in the diagram attached to this answer, the following can be observed:
By comparing ΔDEF and ΔGFH
DF = DG + GF
= 12 + 4
DF = 16
Also,
EF = EH + HF
= 9 + 3
EF = 12
Comparing the sides of ΔDEF and ΔGFH, we have;
[tex]\dfrac{DF}{GF}[/tex] = [tex]\dfrac{EF}{HF}[/tex]
[tex]\dfrac{16}{4}=\dfrac{12}{3}[/tex]
4 = 4
Thus, the two triangles have similar sides.
Comparing the included angle <DFE and <GFH, then;
∠DFE is congruent to ∠GFH
Therefore, to prove that △DFE ~ △GFH by the SAS similarity theorem;
[tex]\dfrac{DF}{GF}[/tex] =[tex]\dfrac{EF}{HF}[/tex] and ∠DFE is congruent to ∠GFH.
Learn more about congruency at
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